Restore the ability of certain rebels to serve in the government (2/3
majority in both the House and the Senate — 14th Amendment)

Approval of removal of the President from his position after the Vice
President and the Cabinet approve such removal and after the President
contests the removal (2/3 majority in both the House and the Senate 25th Amendment)

Additionally, it should be noted the in a few cases, the Constitution
requires a super-majority for a quorum. A quorum is that number of members of a
body that are required for the body to do any work. For example, there is
usually a 50% quorum requirement in the House and Senate — at least half
the members must be present. In the Constitution, super-majority quorums are
required as follows:

Choice of a President in the House when no majority of electoral votes is
achieved (member or members from 2/3 of the states 12th Amendment)

Choice of a Vice President in the Senate when no majority of electoral
votes is achieved (2/3 of all Senators 12th
Amendment)